Good scaling of the CES algorithm with the dimension of the parameter space will be of critical importance for moving beyond the current, low-dimensional proof-of-concept setting. Each stage of the CES algorithm scales to higher dimensions: For the calibration stage, ensemble methods scale well to high-dimensional state and parameter spaces, typically with \(O(10^2)\)  forward model runs [1]}, [2]}, if used with localization. In high dimensions, regularization is also typically needed in calibration algorithms, and various regularization schemes can be added [3]}, [4]}, [5]}, [6]}, [7]}.
The sampling stage also scales well to high dimensions. In particular, MCMC methods scale to non-parametric (infinite-dimensional) problems,
in which the unknown is a function [8]}.
The current bottleneck for scalability lies with the GP emulator, which does not scale easily to high-dimensional inputs. However, other supervised machine learning techniques have potential to do so. For example, random feature maps and deep neural networks show promise in this regard [9]}, [10]}; incorporating these tools in the CES algorithm is a direction of current research.
